In the forties and fifties, there were many superheroes. Mr. Incredible was among the most famous, possessing tremendous strength and near-invulnerability. Elastigirl, a renowned heroine, had the ability to stretch and contort her body to three quarters of an inch thick.
Thanks to the controversy that built up after Mr. Incredible saved a man that didn't want to be saved, and many other complaints about collateral damage, all of the Supers were eventually forced to go into hiding.
While in hiding, Mr. Incredible and Elastagirl got married and had three children. Their children, who also are endowed with super powers, are named Violet, Dash, and Jack Jack. Violet has the ability to generate violet-colored force fields that can withstand great pressure. Dash has the ability to run at mach-level speeds and agility, which allows him run on water. Jack Jack, the youngest, has no clear power. (He is shown to have fluctuating powers.) Among these powers, Jack Jack is able to change his body when in danger. When Syndrome had him, he turned into a devil, then became solid as steel. His powers are apparently linked to his age, as infant superhumans commonly display a wide array of abilities that they will eventually grow out of.
Pixar was initially sued by Marvel, as they believed the Incredibles were too similar to the Fantastic Four.